Rifted passive margins exhibit a large variety in the timing, distribution, and amount of magmatism. The factors controlling magmatism during rifted margin formation, remain, however, incompletely understood, partly owing to the complex rifting styles. In this study, we use 2‐Dimensional numerical models to investigate the effects of depth‐dependent wide rifting and lithospheric counterflow on magmatism during rifted margin formation. Results show that a strong crust promotes narrow margins with a sharp transition to normal thickness oceanic crust whereas a weak crust promotes depth‐dependent wide rifting, with preferential removal of mantle lithosphere, leading to formation of wide margins with over‐thickened (>18 km) igneous crust in the distal margin. Counterflow of depleted lithospheric mantle, in contrast, may delay syn‐rift magmatism, and result in exhumed a‐magmatic continental mantle at narrow margins. The combination of wide rifting and lithospheric counterflow results in magma‐poor wide margins, with in some cases a transition to excess magmatic activity at breakup. Our models provide an explanation for the contrasting magmatic productivity at narrow and wide rifted margins, such as observed in the Lofoten‐Vesterålen, Newfoundland, Kwanza Basin, and Orange Basin margins.